What is the difference between disks and washers

Shell Method: Volume of Solid of Revolution. Log in Sign up. Difference between disc method, washer method and shell meth [Solved! Relevant page 4. The cone generated as a solid of revolution by revolving a right triangle around a vertical axis. Tissue paper decorations that unfold from flat to round are examples of solids of revolution.

Watch the next few seconds of the video below to see how it unfolds in real time. Suppose S is a solid of revolution generated by a region R in the plane. There are two related formulas, depending on how complicated the region R is. Now imagine cutting the solid into thin slices perpendicular to the x -axis.

Each slice looks like a disk or cylinder, except that the outer surface of the disk may have a curve or slant. In fact, I like to think of each disk as being generated by revolving a thin rectangle around the x -axis.

Then you can see that the height of the rectangle, y , is the same as the radius of the disk. The radius is y , which itself is just the function value at x. The height of the disk is equal to dx think of the disk as a cylinder standing on edge. This calculation gives the approximate volume of a thin slice of S. Geometrically, we know that the surface area of a cylinder is found by multiplying the circumference of the circular base times the height of the cylinder.

And if we revolve an infinite number of cylinders, then the result is the volume of the solid. And we sum an infinite number of cylinders by. As the graphic below nicely illustrates, there is a considerable distinction between the disk method and the shell method. So, as we saw with the example above, finding volume using the disk or washer method will produce the same result when calculating using the shell method.

Consequently, the techniques are interchangeable, and it comes down to personal preference as to which integration technique you utilize. How do you find the volume of a solid that is generated by rotating the region enclosed by the How do you find the volume of the solid generated by revolving the region bounded by the graph See all questions in Determining the Volume of a Solid of Revolution.